T(3,3)=2 because we have (i) a tree with 3 edges hanging from the root and (ii) a tree with one edge hanging from the root, at the end of which 2 edges are hanging.

Triangle starts:

1;

0,1;

1,0,1;

0,3,0,2;

2,0,8,0,4;

MAPLE

G:=1/2/(z^2+t*z)*(t*z+1-sqrt(1-2*t*z-3*t^2*z^2-4*z^2-4*t*z^3)): Gserz:=simplify(series(G, z=0, 14)):P[0]:=1: for n from 1 to 12 do P[n]:=sort(expand(coeff(Gserz, z^n))) od: for n from 0 to 12 do seq(coeff(t*P[n], t^k), k=1..n+1) od; # yields the sequence in triangular form